Stability of nonlinear stochastic systems with delayed impulses under self-triggered impulsive control

This paper investigates the stability problem of nonlinear stochastic systems with delayed impulses based on a self-triggered impulsive control (STIC) strategy. By employing the Lyapunov method, an explicit self-triggering mechanism (STM) with state-dependent waiting time parameters is designed, which ensures system stability while effectively avoiding Zeno behavior. Compared with traditional event-triggered impulsive control (ETIC) methods, this strategy does not require continuous state monitoring and can determine the next triggering instant based on the currently available state information. Furthermore, the developed theoretical results are applied to the STIC problem of nonlinear stochastic systems. Finally, the effectiveness and feasibility of the proposed method are validated through two numerical examples.